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Anomalous scaling in an age-dependent branching model

Stephanie Keller-Schmidt1, Murat Tuğrul2, Víctor M. Eguíluz3, Emilio Hernández-García3, and Konstantin Klemm1,4,5,6

  • 1Bioinformatics, Institute of Computer Science, University Leipzig, Härtelstr. 16-18, 04107 Leipzig, Germany
  • 2IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
  • 3IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain
  • 4Bioinformatics and Computational Biology, University of Vienna, Währingerstraße 29, 1090 Vienna, Austria
  • 5Theoretical Chemistry, University of Vienna, Währingerstraße 17, 1090 Vienna, Austria
  • 6School of Science and Technology, Nazarbayev University, Kabanbay Batyr Ave. 53, 010000 Astana, Kazakhstan

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Phys. Rev. E 91, 022803 – Published 2 February, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.022803

Abstract

We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ−α. Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)2. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.

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Outline

Information

Phys. Rev. E 91, 022803– Published 2 February, 2015
  • Received 4 October 2013
  • Revised 23 May 2014

©2015 American Physical Society

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